That's technically true of the exact version of the proof usually presented, but it's a really bad example of a nonconstructive proof, because it can trivially be made constructive by taking the least integer greater than PN that is a factor of (P1*...*PN)+1 as your new prime.
It constructs a number that is not divisible by any member of the list, so either it is prime, or there is some other prime that is not a member of the list. Either way we can grow the list.
